MCQ: HCF & LCM - 2 - SSC CGL MCQ

# MCQ: HCF & LCM - 2 - SSC CGL MCQ

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## 15 Questions MCQ Test - MCQ: HCF & LCM - 2

MCQ: HCF & LCM - 2 for SSC CGL 2024 is part of SSC CGL preparation. The MCQ: HCF & LCM - 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: HCF & LCM - 2 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: HCF & LCM - 2 below.
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MCQ: HCF & LCM - 2 - Question 1

### The product of two numbers is 2028 and their HCF is 13. The number of such pairs is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 1

Here, HCF = 13
Let the numbers be 13x and 13y where x and y are Prime to each other.
Now, 13x × 13y = 2028

The possible pairs are : (1, 12), (3, 4), (2, 6)
But the 2 and 6 are not co-prime.
∴ The required no. of pairs = 2

MCQ: HCF & LCM - 2 - Question 2

### LCM of two numbers is 2079 and their HCF is 27. If one of the number is 189, the other number is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 2

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,

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MCQ: HCF & LCM - 2 - Question 3

### The LCM of two numbers is 520 and their HCF is 4. If one of the number is 52, then the other number is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 3

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × second number = HCF × LCM
⇒ 52 × second number = 4 × 520

MCQ: HCF & LCM - 2 - Question 4

The H.C.F and L.C.M of two numbers are 12 and 336 respectively. If one of the number is 84, the other is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 4

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × second number = HCF × LCM
⇒ 84 × second number = 12 × 336

MCQ: HCF & LCM - 2 - Question 5

Product of two co-prime numbers is 117. Then their L.C.M. is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 5

HCF of two-prime numbers = 1
∴ Product of numbers = their LCM = 117
117 = 13 × 9 where 13 & 9 are co-prime. L.C.M (13,9) = 117.

MCQ: HCF & LCM - 2 - Question 6

The HCF of two numbers is 15 and their LCM is 225. If one of the number is 75, then the other number is :

Detailed Solution for MCQ: HCF & LCM - 2 - Question 6

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × Second number = HCF × LCM
⇒ 75 × Second number = 15 × 225

MCQ: HCF & LCM - 2 - Question 7

The H.C.F. and L.C.M. of two 2- digit numbers are 16 and 480 respectively. The numbers are :

Detailed Solution for MCQ: HCF & LCM - 2 - Question 7

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
H.C.F. of the two 2-digit numbers = 16
Hence, the numbers can be expressed as 16x and 16y, where x and y are prime to each other.
Now,
First number × second number = H.C.F. × L.C.M.
⇒ 16x × 16y = 16 × 480

The possible pairs of x and y, satisfying the condition xy = 30 are : (3, 10), (5, 6), (1, 30), (2, 15)
Since the numbers are of 2-digits each.
Hence, admissible pair is (5, 6)
∴ Numbers are : 16 × 5 = 80 and 16 × 6 = 96

MCQ: HCF & LCM - 2 - Question 8

The product of two numbers is 4107. If the H.C.F. of the numbers is 37, the greater number is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 8

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,

Obviously, numbers are 111 and 37 which satisfy the given condition.
Hence, the greater number = 111

MCQ: HCF & LCM - 2 - Question 9

The product of two numbers is 2160 and their HCF is 12. Number of such possible pairs is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 9

HCF = 12
Numbers = 12x and 12y
where x and y are prime to each other.
∴ 12x × 12y = 2160

= 15 = 3 × 5, 1 × 15
Possible pairs = (36, 60) and (12, 180)

MCQ: HCF & LCM - 2 - Question 10

The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 10

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
We know that,
First number × Second number = LCM × HCF

MCQ: HCF & LCM - 2 - Question 11

The HCF and product of two numbers are 15 and 6300 respectively. The number of possible pairs of the numbers is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 11

Let the number be 15x and 15y, where x and y are co –prime.
∴ 15x × 15y = 6300

So, two pairs are (7, 4) and (14, 2)

MCQ: HCF & LCM - 2 - Question 12

The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.?

Detailed Solution for MCQ: HCF & LCM - 2 - Question 12

HCF of two numbers is 8.
This means 8 is a factor common to both the numbers. LCM is common multiple for the two numbers, it is divisible by the two numbers. So, the required answer = 60

MCQ: HCF & LCM - 2 - Question 13

The HCF and LCM of two numbers are 18 and 378 respectively. If one of the number is 54, then the other number is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 13

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,

MCQ: HCF & LCM - 2 - Question 14

The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?

Detailed Solution for MCQ: HCF & LCM - 2 - Question 14

LCM = 2 × 2 × 2 × 3 × 5
Hence, HCF = 4, 8, 12 or 24
According to question
35 cannot be H.C.F. of 120.

MCQ: HCF & LCM - 2 - Question 15

The product of two numbers is 216. If the HCF is 6, then their LCM is

Detailed Solution for MCQ: HCF & LCM - 2 - Question 15

Let the numbers be 6x and 6y where x and y are prime to each other.
∴ 6x × 6y = 216

∴ LCM = 6xy = 6 × 6 = 36

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